Subcubic triangle-free graphs have fractional chromatic number at most 14/5

Every subcubic triangle-free graph on n vertices contains an independent
set of size at least 5n/14 (Staton'79). We strengthen this result by showing
that all such graphs have fractional chromatic number at most 14/5,
thus confirming a conjecture by Heckman and Thomas. (Joint work with J.-S. Sereni and J. Volec)